Tuesday, October 11, 2011

Crazy economic models

**UPDATED AT END OF POST**

In a recent post I commented on the "fetish of rationality" present in a great deal of mathematical economic theory. Agents in the theories are often assumed to have super-human reasoning abilities and to determine their behaviour and expectations solely through completely rational calculation. In comments, Relja suggested that maybe I'd gone too far and that economists version of rationality isn't all that extreme:

I think critiques like this about rationality in economics miss the point. The rationality assumed in economics is concerned with general trends; generally people pursue pleasure, not pain (according to their own utility functions), they prefer more money to less (an expanded budget constraint leaves them on a higher indifference curve, thus better off), they have consistent preferences (when they're in the mood for chocolate, they're not going to choose vanilla). Correspondingly, firms have the goal of profit maximization - they produce products that somebody will want to buy or they go out of business. Taking the rationality assumption to its "umpteenth" iteration is really quite irrational in itself. A consumer knows that spending 6 years to calculate the mathematically optimal choice of ice-cream is irrational. An economist accordingly knows the same thing. And although assumptions are required for modelling economic scenarios (micro or macro), I seriously doubt that any serious economist would make assumptions that infer such irrationality. :).

I think Relja expressed a well-balanced perspective, has learned some economics in detail, and has taken away from it some conclusions that are, all in all, pretty sound. Indeed, people are goal oriented, don't (usually) prefer pain, and businesses do try to make profits (although whether they try to 'maximize' is an open question). If economists were really just following these reasonable ideas, I would have no problem.

But I also think the problem is worse than Relja may realize. The use of rationality assumptions is more extreme than this, and also decisive in some of the most important areas of economic theory, especially in macroeconomics. A few days ago, John Kay offered this very long and critical essay on the form of modern economic theory. It's worth a read all the way through, but in essence, Kay argues that economics is excessively based on logical deduction of theories from a set of axioms, one of which (usually) is the complete rationality of economic agents:

Rigour and consistency are the two most powerful words in economics today.... They have undeniable virtues, but for economists they have particular interpretations. Consistency means that any statement about the world must be made in the light of a comprehensive descriptive theory of the world. Rigour means that the only valid claims are logical deductions from specified assumptions. Consistency is therefore an invitation to ideology, rigour an invitation to mathematics. This curious combination of ideology and mathematics is the hallmark of what is often called ‘freshwater economics’ – the name reflecting the proximity of Chicago, and other centres such as Minneapolis and Rochester, to the Great Lakes.

Consistency and rigour are features of a deductive approach, which draws conclusions from a group of axioms – and whose empirical relevance depends entirely on the universal validity of the axioms.

Kay isn't quite as explicit as he might have been, but economist Michael Woodford, in a comment on Kay's argument, goes further in spelling out what Key finds most objectionable -- the so-called rational expectations framework, originally proposed by Robert Lucas, which forms the foundations of today's DGSE (dynamic stochastic equilibrium models). A core assumption of such models is that all individuals in the economy have rational expectations about the future, and that such expectations affect their current behaviour.

Now, if this meant something like Relja's comment suggests it might -- that people are simply forward looking, as we know they are -- this would be fine. But it's not. The form this assumption ultimately takes in these models is to assume that everyone in the economy has fully rational expectations, in that they form their expectations in accordance with the conceivably best and most accurate economic models, even if solving those models might require considerable mathematics and computation (and knowledge of everyones' expectations). As Woodford puts it in his comment,

It has been standard for at least the past three decades to use models in which not only does the model give a complete description of a hypothetical world, and not only is this description one in which outcomes follow from rational behavior on the part of the decision makers in the model, but the decision makers in the model are assumed to understand the world in exactly the way it is represented in the model. More precisely, in making predictions about the consequences of their actions (a necessary component of an accounting for their behavior in terms of rational choice), they are assumed to make exactly the predictions that the model implies are correct (conditional on the information available to them in their personal situation).

This postulate of “rational expectations,” as it is commonly though rather misleadingly known, is the crucial theoretical assumption behind such doctrines as “efficient markets” in asset pricing theory and “Ricardian equivalence” in macroeconomics.

It is precisely here that modern economics takes the assumption of rationality much too far merely for the sake of mathematical and theoretical rigour. Do economists really believe people form their expectations in this way? It's hard to imagine they could as the live the rest of their lives with people who do not do this. But the important question isn't what they really believe but on what do they base their theories which then get used by governments in policy making? Sadly, these unrealistic assumptions remain in the key models. But these assumptions really have zero plausibility. Woodford again,

[The rational expectations assumption] is often presented as if it were a simple consequence of an aspiration to internal consistency in one’s model and/or explanation of people’s choices in terms of individual rationality, but in fact it is not a necessary implication of these methodological commitments. It does not follow from the fact that one believes in the validity of one’s own model and that one believes that people can be assumed to make rational choices that they must be assumed to make the choices that would be seen to be correct by someone who (like the economist) believes in the validity of the predictions of that model. Still less would it follow, if the economist herself accepts the necessity of entertaining the possibility of a variety of possible models, that the only models that she should consider are ones -- in each of which everyone in the economy is assumed to understand the correctness of that particular model, -- rather than entertaining beliefs that might (for example) be consistent with one of the other models in the set that she herself regards as possibly correct.

This is the sense in which hyper-rationality really does enter into economic theories. It's still pervasive, and still indefensible. It would be infinitely preferable if macro-economists such as Lucas and his followers (one of whom, Thomas Sargent, was perversely and outrageously just awarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel).

**UPDATE**

Blogger sometimes doesn't seem to register comments. Email alerted me to a sharp criticism by ivansml of some of the points I made, but the comment isn't, at least for my browser, yet showing up. Just so it doesn't get lost, ivansml said:

Every assumption is false when understood literally, including rational expectations. The important thing is whether people behave as if they had rational expectations - and answer to that will fortunately depend on particular model and data, not on emotional arguments and expressive vocabulary.

By the way, if you reject RE but accept that expectations matter and should be forward-looking, how do you actually propose to model them? One possible alternative is to have agents who estimate laws of motion from past data and continously update their estimates, which is something that macroeconomists have actually investigated before. And guess what - this process will often converge to rational expectations equilibrium.

Finally, the comment about Nobel Prize (yeah, it's not real Nobel, whatever) for Sargent is a sign of ignorance. Sargent has published a lot on generalizations or relaxations of RE, including the learning literature mentioned above, literature on robustness (where agents distrust their model and choose actions which are robust to model misspecifications) and even agent-based models. In addition to that, the prize citation focuses on his empirical contributions (i.e. testing theories against data). This does not seem like someone who is religiously devoted to "hyper-rationality" and ideology.

To points in response:

1. Yes, the point is precisely to include expectations but to model their formation in some more behaviourally realistic way, through learning algorithms as suggested. I am aware of such work and think it is very important. Indeed, the latter portion of this post from earlier this year looked precisely at this and considered a recent review of work in this area by Cars Hommes and others. The idea is not to assume that everyone forms their expectations identically, that learning is important, that their may be systematic biases and so on. As ivansml notes, there are circumstances in which the model may settle into a rational expectations equilibrium. But there are also many in which it does not. My hunch -- not backed by any evidence that I can point to readily -- is that the rational expectations equilibrium will be increasingly unlikely as the decisions faced by agents in the model become increasingly complex. Very possibly the system won't settle into any equilibrium at all.

But I think ivansml for pointing this out. It is certainly the case that expectations matter, and these should be brought into theory in some plausible and convincing way. Just to finish on this point, this is a quote from the Hommes review article, suggesting that the RE equilibrium doesn't come up very often:

Learning to forecast experiments are tailor-made to test the expectations hypothesis, with all other model assumptions computerized and under control of the experimenter. Different types of aggregate behavior have been observed in different market settings. To our best knowledge, no homogeneous expectations model [rational or irrational] fits the experimental data across different market settings. Quick convergence to the RE-benchmark only occurs in stable (i.e. stable under naive expectations) cobweb markets with negative expectations feedback, as in Muth's (1961) seminal rational expectations paper. In all other market settings persistent deviations from the RE fundamental benchmark seem to be the rule rather than the exception.

2. On his second point about Thomas Sargent, I plead guilty. ivansml is right -- his work is not as one dimensional as my comments made it seem. Indeed, I had been looking into his work over the past weekend for different reasons and had noticed that his work has been fairly wide ranging, and he does deserve credit for trying to relax RE assumptions. (Although he did seem a little snide in one interview I read, suggesting that mainstream macro-economists were not at all surprised by the recent financial crisis.)